NTA Abhyas 2020
Exam NTA Abhyas
Year 2020
Subject Chemistry
Chapter States of Matter NTA Abhyas 2020 · Chemistry · States of Matter
At 400 K, the root mean square (rms) speed of a gas X (molecular...
At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is
Step-by-step solution
v r m s {v}_{rms} v r m s of
X = 3 R T x M x ; v m p X = \sqrt{\dfrac{3R{T}_{x}}{{M}_{x}}}; {v}_{mp} X = M x 3 R T x ; v m p of Y
= 2 R T y M y = \sqrt{\dfrac{2R{T}_{y}}{{M}_{y}}} = M y 2 R T y Given
v r m s = v m p {v}_{rms} = {v}_{mp} v r m s = v m p 3 R T x M x = 2 R T y M y \sqrt{\dfrac{3R{T}_{x}}{{M}_{x}}} = \sqrt{\dfrac{2R{T}_{y}}{{M}_{y}}} M x 3 R T x = M y 2 R T y M y = 2 R T y M x 3 R T x = 2 × 60 × 40 3 × 400 = 4 {M}_{y} = \dfrac{2R{T}_{y}{M}_{x}}{3R{T}_{x}} = \dfrac{2 \times 60 \times 40}{3 \times 400} = 4 M y = 3 R T x 2 R T y M x = 3 × 400 2 × 60 × 40 = 4
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